Heard the word 'nepers' after many decades. Are you by any chance an Electrical major ?
Thanks for your comment. To be fair, I had not done due diligence before asking. There's a Wikipedia pages on quaternion calculus.
Complex analysis (calculus on functions from 2D rotations to 2D rotations) is beautiful -- Once differentiability guarantees infinite differentiability. Wondering what would the analogue of that be for quaternions
Conformal mappings are not nearly as rich in >2 dimensions. There is a much stronger rigidity constraint and you end up limited to just Möbius transformations. The 2 dimensional case is special.
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[ 14.2 ms ] story [ 55.4 ms ] threadVisualizing quaternions (2018) - https://news.ycombinator.com/item?id=38043644 - Oct 2023 (42 comments)
Visualizing quaternions: an explorable video series (2018) - https://news.ycombinator.com/item?id=31083042 - April 2022 (15 comments)
Visualizing quaternions: An explorable video series - https://news.ycombinator.com/item?id=18310788 - Oct 2018 (32 comments)
On MacOS: no audio on Safari, worked in Chrome though.
I was odd to me to see that Ben Eater was involved. His talents are broad.
Is there such a thing as quaternion analysis -- calculus of functions from quaternions to quaternions.
What would be their key theorems ? What would be the analogue of conformal mappings, if any ?
Any book recommendations would be gratefully appreciated.
There are also these notes: https://www.geometrictools.com/Documentation/Quaternions.pdf
Thanks for your comment. To be fair, I had not done due diligence before asking. There's a Wikipedia pages on quaternion calculus.
Complex analysis (calculus on functions from 2D rotations to 2D rotations) is beautiful -- Once differentiability guarantees infinite differentiability. Wondering what would the analogue of that be for quaternions
See: https://en.wikipedia.org/wiki/Liouville's_theorem_(conformal...